It's true that some people think this. Other people think the 1st Amendment exists for a reason less simplistic than "a government shouldn't censor people," something to do with a healthy human society: https://theintercept.com/2014/08/21/twitter-facebook-executi...

This is not to argue that the 1st Amendment should compel anything beyond protection from government censorship, but that the value it exists to promote applies to wider situations